A Hölder estimate for nonlinear parabolic systems of \(p\)-Laplacian type
The Hölder continuity of the solution \(u= (u^1,u^2,\dots, u^n)\) of the parabolic system \[ {\partial u^j\over\partial t}- \text{div}(|Du|^{p-2} Du^j)= \text{div}(|g|^{p-2} g^j)+ F^j(x,t,Du), \] \(j= 1,2,\dots, n\), is proved under fairly general assumptions on the right-hand side. Here \(p>{2N\over N+2}\) and the functions are defined in a bounded domain in \(\mathbb{R}^{N+1}\). The proof of the main theorem about local Hölder continuity is based on the ``Campanato perturbation'' and diBenedetto's intrinsic scaling. This extends results of diBenedetto, Y.-Z. Chen, Acerbi, and Mingione.
scientific article; zbMATH DE number 6117526